Estimation of the area under ROC curve with censored data. (English) Zbl 1156.62025
Summary: The area under the receiver operating characteristic curve is the most commonly used summary measure of diagnostic accuracy for a continuous-scale diagnostic test. We develop methods to estimate the area under the curve (AUC) with censored data. Based on two different integration representations of this parameter, two nonparametric estimators are defined by the “plug in” method. Both the proposed estimators are shown to be asymptotically normal based on counting process and martingale theory. A simulation study is conducted to evaluate the performances of the proposed estimators.
MSC:
| 62G05 | Nonparametric estimation |
| 62G20 | Asymptotic properties of nonparametric inference |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 62M99 | Inference from stochastic processes |
| 62N02 | Estimation in survival analysis and censored data |
References:
| [1] | Bamber, D. C., The area above the ordinal dominance graph and the area below the receiver operating characteristic curve graph, J. Math. Psychol., 12, 387-412 (1975) · Zbl 0327.92017 |
| [2] | Breslow, N. E.; Edler, L.; Breger, J., A two-sample censored data rank test for acceleration, Biometrics, 40, 1049-1062 (1984) · Zbl 0562.62042 |
| [3] | Fleming, T. P.; Harrington, D. P., Counting Processes and Survival Analysis (1991), Springer: Springer New York · Zbl 0727.62096 |
| [4] | Fleming, T. P.; O’Fallon, J. R.; O’Brien, P. D.; Harrington, D. P., Modified Kolmogorov-Smirnov test procedures with application to arbitrarily right-censored data, Biometrics, 36, 607-625 (1980) · Zbl 0453.62037 |
| [5] | Griner, P. F.; Mayewski, R. J.; Mushlin, A. I., Selection and interpretation of diagnostic tests and procedures, Ann. Internat. Med., 94, 557-600 (1981) |
| [6] | Heagerty, P. J.; Lumley, T.; Pepe, M. S., Time-dependent ROC curves for censored survival data and a diagnostic marker, Biometrics, 56, 337-344 (2000) · Zbl 1060.62622 |
| [7] | Kaplan, E.; Meier, R., Nonparametric estimation from incomplete observations, J. Statist. Assoc., 53, 457-481 (1958) · Zbl 0089.14801 |
| [8] | Major, P.; Rejto, L., Strong embedding of the estimator of the distribution function under random censorship, Ann. Statist., 16, 1113-1132 (1988) · Zbl 0667.62024 |
| [9] | Munk, A., Equivalence and interval testing for Lehmann’s alternative, J. Amer. Assoc., 91, 1187-1195 (1996) · Zbl 0880.62051 |
| [10] | Qin, Y. S., Semiparametric likelihood ratio confidence intervals for various differences of two populations, Statist. Probab. Lett., 33, 135-143 (1997) · Zbl 0902.62026 |
| [11] | Qin, G. S.; Zhou, X.-H., Empirical likelihood inference for the area under the ROC curve, Biometrics, 62, 613-622 (2006) · Zbl 1097.62099 |
| [12] | Richardson, D. S., Measures of skill and value of ensemble prediction systems, their interrelationship and the effect of ensemble size, Quart. J. Roy. Meteor. Soc., 127, 2473-2489 (2001) |
| [13] | Shorack, G. R.; Wellner, J. A., Empirical Processes with Applications to Statistics (1986), Wiley: Wiley New York · Zbl 1170.62365 |
| [14] | Wang, Q. H., Some large sample results for a class of functionals of Kaplan-Meier estimator, Acta Math. Sinica, 14, 191-200 (1998) · Zbl 0899.62065 |
| [15] | Wellek, S., A new approach to equivalence assessment in standard comparative bioavailability trials by means of the Mann-Whitney statistics, Biometrics J., 38, 695-710 (1996) · Zbl 0860.62099 |
| [16] | Wolfe, D. A.; Hogg, R. V., On constructing statistics and reporting data, Amer. Statist., 25, 27-30 (1971) |
| [17] | Zhou, Y.; Liang, H., Empirical likelihood-based semiparametric inference of the treatment effect in the two-sample problem with censoring, Biometrika, 92, 271-282 (2005) · Zbl 1094.62128 |
| [18] | Zweig, M. H.; Campbell, G., Receiver operating characteristic (ROC) curves plots: a fundamental evaluation toll in clinical medicine, Chinese Chem., 39, 561-577 (1993) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
